Techniques for angle resolution in radar

ABSTRACT

A radar apparatus for estimating position of a plurality of obstacles. The radar apparatus includes a receive antenna unit. The receive antenna unit includes a linear array of antennas and an additional antenna at a predefined offset from at least one antenna in the linear array of antennas. The radar apparatus also includes a signal processing unit. The signal processing unit estimates an azimuth frequency associated with each obstacle of the plurality of obstacles from a signal received from the plurality of obstacles at the linear array of antennas. In addition, the signal processing unit estimates an azimuth angle and an elevation angle associated with each obstacle from the estimated azimuth frequency associated with each obstacle.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/329,446, filed Jul. 11, 2014, which application claims priority fromIndia provisional patent application No. 4825/CHE/2013 filed on Oct. 25,2013, both of which are hereby incorporated by reference in theirentirety.

TECHNICAL FIELD

Embodiments of the disclosure relate generally to radars.

BACKGROUND

A vehicle has parking sensors to detect an obstacle behind the vehicle.The parking sensors determine a distance of the vehicle from theobstacle using ultrasonic signals when backing a vehicle. The parkingsensor operates at ultrasonic frequencies. The parking sensor outputs anultrasonic detecting signal to detect whether any obstacle is behind therear of the vehicle and receives an ultrasonic signal as reply from theobstacle. A vehicle generally requires multiple parking sensors to coverthe entire rear of the vehicle which makes it a cost intensive solution.Also, the ultrasonic parking sensors use a time division obstacledetecting method in which each sensor sends and receives ultrasonicdetect signal in a defined time slot. Thus, the process of detectingobstacles using ultrasonic sensors is time consuming which is unsafe invehicles moving with high velocity.

Ultrasonic parking sensors require the measurement and drilling of holesin the vehicle's bumper to install transducers. There are risksassociated with drilling and mounting the transducers into the bumper.The performance of the Ultrasonic sensors is sensitive to temperatureand atmospheric conditions such as snow and rain. The performance ofultrasonic sensors is severely degraded when the sensors are coveredwith snow. In addition, the range over which the ultrasonic sensorsoperates is limited.

The use of radars in automotive applications is evolving rapidly. Radarsdo not have the drawbacks discussed above in the context of ultrasonicsensors. Radar finds use in number of applications associated with avehicle such as collision warning, blind spot warning, lane changeassist, parking assist and rear collision warning. Pulse radar and FMCW(Frequency Modulation Continuous Wave) radar are predominantly used insuch applications. In the pulse radar, a signal in the shape of a pulseis transmitted from the radar at fixed intervals. The transmitted pulseis scattered by the obstacle. The scattered pulse is received by theradar and the time between the transmission of the pulse and receivingthe scattered pulse is proportional to a distance of the radar from thetarget. For better range resolution, a narrower pulse is used whichrequires a high sampling rate in an ADC (analog to digital converter)used in the pulse radar. In addition, sensitivity of a pulse radar isdirectly proportional to the power which complicates the design processof the pulse radar.

In an FMCW radar, a transmit signal is frequency modulated to generate atransmit chirp. An obstacle scatters the transmit chirp. The scatteredchirp is received by the FMCW radar. A signal obtained by mixing thetransmitted chirp and the received scattered chirp is termed as a beatsignal. The frequency of the beat signal is proportional to the distanceof the obstacle from the FMCW radar. The beat signal is sampled by ananalog to digital converter (ADC). A sampling rate of the ADC isproportional to the maximum frequency of the beat signal and thefrequency of the beat signal is proportional to the range of thefarthest obstacle which can be detected by the FMCW radar. Thus, unlikein the pulse radar, the sampling rate of the ADC in the FMCW radar isindependent of the range resolution.

Typically in an FMCW radar, multiple chirps are transmitted in a unitcalled as frame. A 2-dimensional (2D) FFT is performed on the sampledbeat signal data received over a frame for range and relative velocityestimation of the obstacle. A bin is a 2D FFT grid that corresponds to arange and relative velocity estimate of an obstacle. A signal detectedin a specific bin represents the presence of an obstacle with apredefined range and relative velocity. When multiple receive antennasare used to receive the scattered chirp, the FMCW radar estimates anelevation angle of the obstacle and an azimuth angle of the obstacle. Ineach frame, a 2D FFT is computed using the data received from eachreceive antenna. Thus, the number of 2D FFT's is equal to the number ofthe receive antennas. When an obstacle is detected in a specific bin ofthe 2D FFT grid, the value of the specific bin corresponding to each ofthe receive antennas is used to estimate the azimuth angle and theelevation angle of the obstacle.

The FMCW radar resolves obstacles in the dimensions of range, relativevelocity and angle. To accurately estimate position of the obstacle, itis required that the obstacle is resolved in any one of thesedimensions. Thus, if there are multiple obstacles at the same distancefrom the FMCW radar and travelling with same relative velocity, the FMCWradar is required to resolve these obstacles in angle dimension. Thus,angle estimation is an important factor in determining the performanceof the FMCW radar. The resolution and accuracy of the angle estimationis directly proportional to the number of antennas unit in the FMCWradar. As FMCW radars are used in a broad range of applications, theirdesign becomes more cost-sensitive. Each antenna used to receive thescattered chirp has a distinct receiver path which includes amplifiers,mixers, ADCs and filters. Thus, the number of antennas used in the FMCWradar is a key factor in determining the overall cost of the FMCW radar.Therefore it is important to minimize the number of antennas andprocessing requirements of the FMCW radar and at the same timemaintaining optimum performance level and accuracy.

SUMMARY

This Summary is provided to comply with 37 C.F.R. §1.73, requiring asummary of the invention briefly indicating the nature and substance ofthe invention. It is submitted with the understanding that it will notbe used to interpret or limit the scope or meaning of the claims.

An embodiment provides a radar apparatus for estimating position of aplurality of obstacles. The radar apparatus includes a receive antennaunit. The receive antenna unit includes a linear array of antennas andan additional antenna at a predefined offset from at least one antennain the linear array of antennas. The radar apparatus also includes asignal processing unit. The signal processing unit estimates an azimuthfrequency associated with each obstacle of the plurality of obstaclesfrom a signal received from the plurality of obstacles at the lineararray of antennas. The signal processing unit also estimates a complexamplitude associated with each obstacle from the estimated azimuthfrequency associated with the plurality of obstacles and from the signalreceived from the plurality of obstacles at the linear array ofantennas. The signal processing unit estimates a complex phasorassociated with each obstacle from the estimated complex amplitudeassociated with the plurality of obstacles and from a signal receivedfrom the plurality of obstacles at the additional antenna. In addition,the signal processing unit estimates an azimuth angle and an elevationangle associated with each obstacle from the estimated complex phasorassociated with each obstacle and from the estimated azimuth frequencyassociated with each obstacle.

Another embodiment provides a method of estimating position of aplurality of obstacles using a radar apparatus. The method includesestimating an azimuth frequency associated with each obstacle of theplurality of obstacles from a signal received from the plurality ofobstacles at the radar apparatus. A complex amplitude associated witheach obstacle is estimated from the estimated azimuth frequencyassociated with the plurality of obstacles and from the signal receivedfrom the plurality of obstacles at the radar apparatus. A complex phasorassociated with each obstacle is estimated from the estimated complexamplitude associated with the plurality of obstacles and from the signalreceived from the plurality of obstacles at the radar apparatus. Anazimuth angle and an elevation angle associated with each obstacle areestimated from the estimated complex phasor associated with eachobstacle and from the estimated azimuth frequency associated with eachobstacle.

Additionally, an embodiment provides a radar apparatus for estimatingposition of a plurality of obstacles. The radar apparatus includes atransmit antenna unit. A transmitter is coupled to the transmit antennaunit and generates the outbound RF (radio frequency) signal. The radarapparatus also includes a receive antenna unit. A receiver is coupled tothe receive antenna unit and receives the inbound RF signal from thereceive antenna unit. The outbound RF signal is scattered by theplurality of obstacles to generate the inbound RF signal. A mixer iscoupled to the receiver and to the transmitter and demodulates theinbound RF signal to generate a demodulated signal. An analog to digitalconverter (ADC) is coupled to the mixer and generates a digital signalin response to the demodulated signal received from the mixer. An FFT(fast fourier transform) module coupled to the ADC and transforms thedigital signal from a time domain to a frequency domain. A signalprocessing unit is coupled to the FFT module and processes the digitalsignal. The signal processing unit estimates an azimuth frequencyassociated with each obstacle of the plurality of obstacles from thedigital signal. The signal processing unit also estimates a complexamplitude associated with each obstacle from the estimated azimuthfrequency associated with the plurality of obstacles and from thedigital signal. A complex phasor associated with each obstacle isestimated from the estimated complex amplitude associated with theplurality of obstacles. An azimuth angle and an elevation angleassociated with each obstacle are estimated from the estimated complexphasor associated with each obstacle and from the estimated azimuthfrequency associated with each obstacle.

Other aspects and example embodiments are provided in the Drawings andthe Detailed Description that follows.

BRIEF DESCRIPTION OF THE VIEWS OF DRAWINGS

FIG. 1 illustrates a receive antenna unit in a radar apparatus,according to an embodiment;

FIG. 2(a) illustrates a radar apparatus, according to an embodiment;

FIG. 2(b) illustrates operation of a radar apparatus, according to anembodiment

FIG. 2(c)-1-FIG. 2(c)-2 illustrates beam-width of a transmit antennaunit in a radar apparatus, according to an embodiment; and

FIG. 3 illustrates a radar apparatus, according to an embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 illustrates a receive antenna unit 100 in a radar apparatus,according to an embodiment. In an embodiment, the receive antenna unit100 is integrated in a radar apparatus which is further integrated in anindustrial or automotive application. The receive antenna unit 100includes a linear array of antennas. The linear array of antennasincludes a plurality of antennas, for example, antenna a1, a2, a3 andaN, where aN is the N^(th) antenna and N is an integer. For the sake ofsimplicity and understanding, the plurality of antennas represented inFIG. 1 will be represented as a1-aN further in the description. Thelinear array of antennas a1-aN is represented to be placed along theX-axis. The adjacent antennas in the linear array of antennas a1-aN areseparated by a spacing d i.e. the antennas a1 and a2 are placed atdistance from each other.

The receive antenna unit 100 further includes an additional antenna b1.The additional antenna b1 is at a predefined offset from at least oneantenna in the linear array of antennas a1-aN. The predefined offset is(α, β) from the antenna a1 in the linear array of antennas a1-aN asillustrated in FIG. 1. α is a distance of the additional antenna b1 fromthe Z axis and β is a distance of the additional antenna b1 from the Xaxis. In one embodiment, the additional antenna is not in XZ plane and aperpendicular distance of the additional antenna b1 from the XZ plane isγ. In one embodiment, the predefined offset is a multiple of λ/2, whereλ is an operating wavelength of the receive antenna unit 100. In anembodiment, d is λ/2, α is λ/4, β is λ/2 and γ is 0. In an embodiment,the spacing d between antennas in the linear array of antennas is amultiple of λ/2.

For ease of understanding, we consider an embodiment in which the lineararray of antennas consists of three antennas (a1, a2 and a3). Theequation 1 below is a mathematical representation of the signal receivedat the receive antenna unit 100 from an obstacle 102. It is to be notedthat the signal ‘r’ represented in equation 1 depicts a signal obtainedafter a signal processing unit processes the signal received at thereceive antenna unit 100. In an embodiment, the signal ‘r’ depicts asignal obtained after performing 2D FFT on the signal received at eachantenna in the receive antenna unit 100 from the obstacle.

r=A[1 e ^(−jw) ^(x) e ^(−j2w) ^(x) e ^(−jψ)]   (1)

where, w_(x) is azimuth frequency. A is the complex amplitudecorresponding to the obstacle. ψ is the phase at the additional antennab1 and is given by

$\psi = {w_{z} + {\frac{\alpha}{d}w_{x}}}$

where, w_(z) is elevation frequency. w_(x) and w_(z) are defined as:

$\begin{matrix}{w_{x} = {\frac{2\; \pi}{\lambda}d\; {\sin (\theta)}{\cos (\varphi)}}} & (2) \\{w_{z} = {\frac{2\; \pi}{\lambda}\beta \; {\sin (\varphi)}}} & (3)\end{matrix}$

In equation 1, the component e^(−jw) ^(x) represents a factor as aresult of the antenna a1, the component e^(−j2w) ^(x) represents afactor as a result of the antenna a2 and the component e^(−jψ)represents a factor as a result of the antenna b1. An angle 104 (θ)represents an azimuth angle between the obstacle 102 and the antennaunit 100 and an angle 108 (Φ) represents an elevation angle between theobstacle 102 and the antenna unit 100. The azimuth angle (θ) 104 is anangle between the Y axis and the projection of a vector from antenna a1to the obstacle 102 on the XY plane. The elevation angle (Φ) 108 is anangle between a vector from antenna a1 to the obstacle 102 and the XYplane. The receive antenna unit 100, in an embodiment, is used toestimate position of a plurality of obstacles at a fixed distance fromthe receive antenna unit 100 and having same relative velocity withrespect to the radar apparatus. In one example, the receive antenna unit100 is used to estimate the position of a plurality of obstacles whichare at different distances and have different relative velocities withrespect to the radar apparatus. For example, the receive antenna unit100 is used to estimate a position of two obstacle A and B in which A isat 1 m and B is at 1.2 m from the radar apparatus and the relativevelocity of A is 5 m/s and the relative velocity of B is 4.5 m/s. In anadditional example, the receive antenna unit 100 is used to estimate aposition of two obstacles that are detected in different bins of a 2DFFT grid but their signals in the 2D FFT domain interfere with eachother. For example, a first obstacle which is detected in a first bin ofa 2D FFT grid can have an attenuated signal representing the firstobstacle in a second bin. This attenuated signal interferes withposition estimation of a second obstacle detected in the second bin. Inan embodiment, the receive antenna unit 100 estimates position of upto(N−1) obstacles when the linear array of antennas a1-aN has N antennas.

FIG. 2(a) illustrates a radar apparatus 200, according to an embodiment.The radar apparatus 200 includes a transmit antenna unit 205, a receiveantenna unit 210 and a signal processing unit 215. The receive antennaunit 210 is similar to the receive antenna unit 100 in connection andoperation. The radar apparatus 200 may include one or more additionalcomponents known to those skilled in the relevant art and are notdiscussed here for simplicity of the description.

The operation of the radar apparatus 200 illustrated in FIG. 2(a) isexplained now. The radar apparatus 200 resolves obstacles in thedimensions of range, relative velocity and angle. To accurately estimateposition of the obstacle, it is required that the obstacle is resolvedin any one of these dimensions. Thus, if there are a plurality ofobstacles at the same distance from the radar apparatus 200 and havingsame relative velocity with respect to the radar apparatus 200, theradar apparatus 200 is required to resolve these obstacles in angledimension. The radar apparatus 200 estimates position of a plurality ofobstacles at a fixed distance from the radar apparatus 200 and havingfixed relative velocity with respect to the radar apparatus 200. In oneembodiment, the radar apparatus 200 estimates position of a plurality ofobstacles and each obstacle of the plurality of obstacles is at adifferent distance from the radar apparatus 200. For ease ofunderstanding, the operation of the radar apparatus 200 is explainedwith the help of two obstacles in FIG. 2(b).

FIG. 2(b) illustrates operation of a radar apparatus 200, according toan embodiment. The operation of the radar apparatus 200 is illustratedusing obstacles ‘m’ 255 and ‘n’ 260 of the plurality of obstacles. Alsoit is considered, that the receive antenna unit 210 (in FIG. 2a )includes three antennas a1, a2 and a3 forming the linear array ofantennas and the additional antenna b1. θ_(m) 265 is an azimuth angleassociated with the obstacle ‘m’ 255 and φ_(m) 270 is an elevation angleassociated with the obstacle ‘m’ 255. Similarly, θ_(n) 275 is an azimuthangle associated with the obstacle ‘n’ 260 and φ_(n) 280 is an elevationangle associated with the obstacle ‘n’ 260. It is to be noted that theazimuth angle θ_(n) 275 as depicted in FIG. 2(b) is interpreted as anangle in negative direction.

The transmit antenna unit 205 is configured to transmit an RF (radiofrequency) signal and the receive antenna unit 210 receives a scatteredsignal from the obstacle ‘m’ 255 and ‘n’ 260 of the plurality ofobstacles. The transmitted RF signal comprises a plurality of frames ofthe RF signal generated by the transmitter and the received scattered RFsignal comprises a plurality of frames of the signal received from theplurality of obstacles. The receive antenna unit 210 tracks signal fromthe plurality of obstacles at the plurality of frames and frame ‘k’ isone of the plurality of frames. The signal received at the receiveantenna unit 210 at a frame ‘k’ of the plurality of frames, from theobstacles ‘m’ 255 and ‘n’ 260 is represented as:

$\begin{matrix}{\begin{bmatrix}r_{{a\; 1},k} \\r_{{a\; 2},k} \\r_{{a\; 3},k} \\r_{{b\; 1},k}\end{bmatrix} = {{A_{m,k}\begin{bmatrix}1 \\e^{- {jw}_{xm}} \\e^{{- j}\; 2w_{xm}} \\e^{{- j}\; \psi_{m}}\end{bmatrix}} + {A_{n,k}\begin{bmatrix}1 \\e^{- {jw}_{xn}} \\e^{{- j}\; 2w_{xn}} \\e^{{- j}\; \psi_{n}}\end{bmatrix}}}} & (4)\end{matrix}$

where r_(a1,k) r_(a2,k) r_(a3,k) r_(b1,k) are the signals received atframe k at the antennas a1, a2, a3 and b1 respectively. It is to benoted that r_(a1,k) r_(a2,k) r_(a3,k) r_(b1,k) represents signalreceived at the respective antennas after processing in the signalprocessing unit 215. For example, in an embodiment, the signal r_(a1,k)depicts the signal received from the obstacle ‘m’ 255 and ‘n’ 260 at theantenna a1 for frame k after performing 2D FFT. A_(m,k) and A_(n,k) arethe complex amplitudes of the two obstacles ‘m’ 255 and ‘n’ 260respectively at frame k. w_(xm) is an azimuth frequency associated withthe obstacle ‘m’ 255 and w_(xn) is an azimuth frequency associated withthe obstacle ‘n’ 260. ψ_(m) is referred to as a phase due to theobstacle ‘m’ 255 at the additional antenna b1 and ψ_(n) is referred toas a phase due to the obstacle ‘n’ 260 at the additional antenna b1.Also, e^(−jψ) ^(m) is referred to as a complex phasor associated withthe obstacle ‘m’ 255 at the additional antenna b1 and e^(−jω) ^(n) isreferred to as a complex phasor associated with the obstacle ‘n’ 260 atthe additional antenna b1. The azimuth frequency w_(xm) and w_(xn) aredefined as:

$\begin{matrix}{w_{xm} = {\frac{2\; \pi}{\lambda}d\; {\sin \left( \theta_{m} \right)}{\cos \left( \varphi_{m} \right)}}} & (5) \\{w_{xn} = {\frac{2\; \pi}{\lambda}d\; {\sin \left( \theta_{n} \right)}{\cos \left( \varphi_{n} \right)}}} & (6)\end{matrix}$

An elevation frequency (w_(zm)) associated with the obstacle ‘m’ 255 andan elevation frequency (w_(zn)) associated with the obstacle ‘n’ 260 aredefined as:

$\begin{matrix}{w_{zm} = {\frac{2\; \pi}{\lambda}\beta \; {\sin \left( \varphi_{m} \right)}}} & (7) \\{w_{zn} = {\frac{2\; \pi}{\lambda}\beta \; {\sin \left( \varphi_{n} \right)}}} & (8)\end{matrix}$

The phase (ψ_(m)) due to the obstacle ‘m’ 255 at the additional antennab1 and the phase (ψ_(n)) due to the obstacle ‘n’ 260 at the additionalantenna blare defined as:

$\begin{matrix}{\psi_{m} = {w_{zm} + {\frac{\alpha}{d}w_{xm}}}} & (9) \\{\psi_{n} = {w_{zn} + {\frac{\alpha}{d}w_{xn}}}} & (10)\end{matrix}$

where θ_(m) 265 is the azimuth angle associated with the obstacle ‘m’255 and φ_(m) 270 is the elevation angle associated with the obstacle‘m’ 255. Similarly, θ_(n) 275 is the azimuth angle associated with theobstacle ‘n’ 260 and φ_(n) 280 is the elevation angle associated withthe obstacle ‘n’ 260.

The signal processing unit 215 is configured to estimate the azimuthfrequency associated with each obstacle from the signal received fromthe plurality of obstacles. Thus, the signal processing unit 215estimates azimuth frequency w_(xm) and w_(xn) associated with obstacles‘m’ 255 and ‘n’ 260 respectively, from the signal received from theobstacles ‘m’ 255 and ‘n’ 260 at the linear array of antennas a1, a2 anda3. The estimation of azimuth frequency is performed using one of themany methods know in the art, but not limited to, root MUSIC (multiplesignal classification) method, spectral MUSIC method and methods basedon maximum likelihood estimation. It is to be noted that using thesemethods, a radar apparatus with N antennas can estimate azimuthfrequency of N−1 obstacles. The estimation provides estimated azimuthfrequency w_(xm) and w_(xn) associated with each obstacle i.e. obstacle‘m’ 255 and obstacle ‘n’ 260. The signal processing unit 215 estimatesthe complex amplitude associated with each obstacle from the estimatedazimuth frequency associated with the plurality of obstacles and fromthe signal received from the plurality of obstacles at the linear arrayof antennas a1, a2 and a3. Thus, the signal processing unit 215estimates the A_(m,k) and A_(n,k), the complex amplitudes of the twoobstacles ‘m’ 255 and ‘n’ 260 respectively using equation 4 as follows:

$\begin{matrix}{{{A_{m,k}\begin{bmatrix}1 \\e^{- {jw}_{xm}} \\e^{{- 2}{jw}_{xm}}\end{bmatrix}} + {A_{n,k}\begin{bmatrix}1 \\e^{- {jw}_{xn}} \\e^{{- 2}{jw}_{xn}}\end{bmatrix}}} = \begin{bmatrix}r_{{a\; 1},k} \\r_{{a\; 2},k} \\r_{{a\; 3},k}\end{bmatrix}} & (11) \\{{\underset{\underset{S}{}}{\begin{bmatrix}1 & 1 \\e^{- {jw}_{xm}} & e^{- {jw}_{xn}} \\e^{{- 2}{jw}_{xm}} & e^{{- 2}{jw}_{xn}}\end{bmatrix}}\mspace{11mu}\begin{bmatrix}A_{m,k} \\A_{n,k}\end{bmatrix}} = \underset{\underset{r_{k}{({1:3})}}{}}{\begin{bmatrix}r_{{a\; 1},k} \\r_{{a\; 2},k} \\r_{{a\; 3},k}\end{bmatrix}}} & (12) \\{\begin{bmatrix}A_{m,k} \\A_{n,k}\end{bmatrix} = {{{pinv}(S)}{r_{k}\left( {1\text{:}3} \right)}}} & (13)\end{matrix}$

where, pinv(S) is a pseudo-inverse of S. In one embodiment, pinv(S) isdefined as:

pinv(S)=(S ^(H) S)⁻¹ S ^(H)   (14)

where H is referred to as a conjugate transpose. Estimating pinv(S)involves inverting the 2×2 matrix (S^(H)S) as illustrated in equation14. S is independent of the frame ‘k’. Therefore, once estimated,pinv(S) is used for all the successive frames. r_(a1,k) represents thesignal received at antenna a1 at frame k. Similarly, r_(a2,k) representsthe signal received at the antenna a2 at frame k. The signal processingunit 215 uses the plurality of frames of the signal received at thelinear array of antennas a1, a2 and a3 for estimating the complexamplitude associated with each obstacle. The complex amplitude isestimated for each frame of the plurality of frames. For each frame, avalue of r_(k)(1:3) is measured, which is the signal received from theobstacles ‘m’ 255 and ‘n’ 260 at the linear array of antennas a1, a2 anda3. In an embodiment, the estimate of the complex amplitudes for frame kA_(m,k) and A_(n,k), associated with the obstacles ‘m’ 255 and ‘n’ 260respectively, is a least squares estimate. In another embodiment, theestimate of the complex amplitudes for frame k A_(m,k) and A_(n,k),associated with the obstacles ‘m’ 255 and ‘n’ 260 respectively, is aweighted least squares estimate when an SNR (signal to noise ratio) ateach antenna of the linear array of antennas is different i.e. SNR ata1, a2 and a3 are different or when the SNR at any antenna of the lineararray of antennas a1, a2 and a3 changes across frames. The estimation ofthe complex amplitudes provides estimated complex amplitudes associatedwith each obstacle i.e. obstacle ‘m’ 255 and obstacle ‘n’ 260 for eachframe of the plurality of frames.

The signal processing unit 215 estimates the complex phasor associatedwith each obstacle from the estimated complex amplitude associated withthe plurality of obstacles and from a signal received from the pluralityof obstacles at the additional antenna. Thus, the signal processing unit215 estimates the complex phasor e^(−jψ) ^(m) and e^(−jψ) ^(n)associated with the obstacle ‘m’ 255 and ‘n’ 260 respectively, from thecomplex amplitudes A_(m,k) and A_(n,k), associated with the obstacles‘m’ 255 and ‘n’ 260 respectively and from the signal received from theobstacles ‘m’ 255 and ‘n’ 260 at the additional antenna b1. The signalprocessing unit 215 estimates the complex phasor e^(−jψ) ^(m) ande^(−jψ) ^(n) using equation 4 as follows:

$\begin{matrix}{{{A_{m,k}e^{{jw}_{zm}}} + {A_{n,k}e^{{jw}_{zn}}}} = r_{{b\; 1},k}} & (15) \\{{\underset{\underset{T}{}}{\begin{bmatrix}A_{m,1} & A_{n,1} \\A_{m,2} & A_{n,2} \\\vdots & \vdots \\A_{m,N_{fr}} & A_{n,N_{fr}}\end{bmatrix}}\;\begin{bmatrix}e^{j\; \psi_{m}} \\e^{j\; \psi_{n}}\end{bmatrix}} = \underset{\underset{r_{b\; 1}}{}}{\begin{bmatrix}r_{{b\; 1},1} \\r_{{b\; 1},2} \\\vdots \\r_{{b\; 1},N_{fr}}\end{bmatrix}}} & (16) \\{\begin{bmatrix}e^{j\; \psi_{m}} \\e^{j\; \psi_{n}}\end{bmatrix} = {{{pinv}(T)}r_{b\; 1}}} & (17)\end{matrix}$

where, pinv(T) is a pseudo-inverse of T. In one embodiment, pinv(T) isdefined as:

pinv(T)=(T ^(H) T)⁻¹ T ^(H)   (18)

where H is referred to as a conjugate transpose. Estimating pinv(T)involves inverting the 2×2 matrix (T^(H)T) illustrated in equation 18.Equation 16 represents equation 15 at the plurality of frames ‘k’ i.e.at k=1, 2 . . . N_(fr) where N_(fr) is the N^(th) frame of the pluralityof frames. The signal processing unit 215 uses the signal received atthe additional antenna b1 across the plurality of frames for estimatingthe complex phasor associated with each obstacle. The signal processingunit 215 also uses the estimated complex amplitude associated with theplurality of obstacles across the plurality of frames for estimating thecomplex phasor associated with each obstacle. Thus, A_(m,1) and A_(n,1)in equation 16 represents complex amplitude because of obstacle m atframe 1 and complex amplitude because of obstacle n at frame 1respectively. Similarly, r_(b1,1) represents the signal received at theadditional antenna b1 at frame 1. Similarly, A_(m,Nfr) and A_(n,Nfr) inequation 16 represents complex amplitude because of obstacle m at frameN_(fr) and complex amplitude because of obstacle n at frame N_(fr)respectively. Similarly, r_(b1,Nfr) represents the signal received atthe additional antenna b1 at frame N_(fr). In an embodiment, theestimate of the complex phasor e^(−jψ) ^(m) and e^(−jψ) ^(n) associatedwith the obstacle ‘m’ 255 and ‘n’ 260 respectively, is a least squaresestimate. In another embodiment, the estimate of the complex phasore^(−jψ) ^(m) and e^(−jψ) ^(n) associated with the obstacle ‘m’ 255 and‘n’ 260 respectively, is a weighted least squares estimate when the SNRat the additional antenna varies across the plurality of frames.

The signal processing unit 215 estimates the elevation frequency(w_(zm)) associated with the obstacle ‘m’ 255 and the elevationfrequency (w_(zn)) associated with the obstacle ‘n’ 260 from the complexphasor e^(−jψ) ^(m) and e^(−jψ) ^(n) and from the estimated azimuthfrequency w_(xm) and w_(xn), using the following equations:

$\begin{matrix}{w_{zm} = {{angle}\; \left( {e^{j\; \psi_{m}}e^{{- \frac{\alpha}{d}}w_{xm}}} \right)}} & (19) \\{w_{zn} = {{angle}\; \left( {e^{j\; \psi_{n}}e^{{- \frac{\alpha}{d}}w_{xn}}} \right)}} & (20)\end{matrix}$

The signal processing unit 215 is further configured to estimate theelevation angle φ_(m) 270 and the azimuth angle θ_(m) 265 associatedwith the obstacle ‘m’ 255 from the estimated elevation frequency w_(zm)using equation 7 and equation 5 respectively as shown below:From equation 7:

$\begin{matrix}{\varphi_{m} = {\sin^{- 1}\left( \frac{w_{zm}}{2\; \pi \; {\beta/\lambda}} \right)}} & (21)\end{matrix}$

And from equation 5:

$\begin{matrix}{\theta_{m} = {\sin^{- 1}\left( \frac{w_{xm}}{2\; \pi \; d\; {{\cos \left( \varphi_{m} \right)}/\lambda}} \right)}} & (22)\end{matrix}$

Similarly, the signal processing unit 215 is configured to estimate theelevation angle θ, 280 and the azimuth angle θ, 275 associated with theobstacle ‘n’ 260 from the estimated elevation frequency w_(zn) usingequation 8 and equation 6 respectively. The signal processing unit 215,in one embodiment, estimates the azimuth angle and the elevation anglefrom the estimated complex phasor associated with each obstacle and fromthe estimated azimuth frequency associated with each obstacle.

The radar apparatus 200 provides an efficient method to resolve theazimuth angle and elevation angle of two obstacles ‘m’ 255 and ‘n’ 260which are at a same distance from the radar apparatus 200 and having thesame relative velocity with respect to the radar apparatus 200. Also,the radar apparatus 200 require less number of antennas than theconventional methods. Some conventional methods use a 2D array ofantennas while others use an L shaped antenna with a linear array ofantennas in orthogonal directions to estimate the azimuth angle and theelevation angle of multiple obstacles. In contrast, with N antennas inthe linear array of antennas and with one additional antenna in thereceive antenna unit 210, the radar apparatus 200 is able to estimateazimuth angle and elevation angle of N−1 obstacles that are at the samerange from the radar apparatus 200 and having the same relative velocitywith respect to the radar apparatus 200.

Also, a processing requirement of the signal processing unit 215 in theradar apparatus 200 is low as compared to the existing radar apparatussince the method employed by the signal processing unit 215 allows for aclosed form solution that do not require any search. Consequently theperformance of the radar apparatus 200 is also more robust and does notsuffer from performance degradation due to false peaks or misseddetection of obstacles that severely effect search based solutionsespecially at low SNRs (signal to noise ratio). Further, this methoddoes not require computationally intensive tasks such as findingeigenvalues and eigenvectors or inverting large matrices. The radarapparatus 200 provides an effective method to estimate the azimuth angleand the elevation angle even when an angular separation of the twoobstacles ‘m’ 255 and ‘n’ 260 is small.

FIG. 2(c)-1-FIG. 2(c)-2 illustrates beam-width of a transmit antennaunit 205 in a radar apparatus, according to an embodiment. The transmitantenna unit 205 is similar in connection and operation to the transmitantenna unit 205 in the radar apparatus 200. The transmit antenna unit205 includes a plurality of transmit antennas. For ease of understandingand not for the purpose of limitation, the transmit antenna unit 205 isshown with two transmit antenna Tx1 and Tx2.

As illustrated in FIG. 2(c)-1, the transmit antennas Tx1 and Tx2 operatetogether thus increasing the power and focus of the beam-width 230.Thus, the transmit antenna unit 205 provides a beam-width 230 which isnarrow and has high SNR (signal to noise ratio). This arrangement isused by the radar apparatus 200 for estimating position of an obstacleof the plurality of obstacles in a first range. In an embodiment, thisarrangement is used by the radar apparatus 200 for estimating positionof a far-range obstacle.

As illustrated in FIG. 2(c)-2 and FIG. 2(c)-3, the transmit antennas Tx1and Tx2 operate in a sequence i.e. first Tx1 is activated and Tx2 isinactive and then Tx1 in inactivated and Tx2 is activated. Thebeam-width 235 and 240 produced by Tx1 and Tx2 respectively, is wide andthus used for estimating position of an obstacle close to the radarapparatus 200 and in a wide field of view. Thus, at a given timeinstant, only one transmit antenna of the plurality of transmit antennasis activated. In an embodiment, at a given time instant, a set oftransmit antennas of the plurality of transmit antennas is activated.The arrangement illustrated in FIG. 2(c)-2 and FIG. 2(c)-3 is used bythe radar apparatus 200 for estimating position of an obstacle of theplurality of obstacles in a second range, where the first range isgreater than the second range.

In an embodiment, the arrangement illustrated in FIG. 2(c)-2 and FIG.2(c)-3 is used by the radar apparatus 200 for estimating position of anear-range obstacle, where the far-range is greater than the near-range.In an embodiment, each transmit antenna of the plurality of transmitantennas operate together to estimate position of each obstacle in afirst range and each antenna in the plurality of transmit antennasoperate in a sequence to estimate position of each obstacle in a secondrange, wherein first range is greater than the second range. Thearrangements illustrated in FIG. 2(c)-2 and FIG. 2(c)-3 are used toimprove de-correlation in the received signal across successive framesin the radar apparatus 200. Such de-correlation improves the angleestimation performance of the radar apparatus 200.

In an embodiment, the radar apparatus 200 is installed on a vehicle anda motion in the vehicle improves de-correlation in the radar apparatus200. In an embodiment, the motion is specifically introduced in thevehicle to improve de-correlation in the radar apparatus 200. In anembodiment the motion introduced is of the order of the wavelength ofthe RF signal transmitted by the radar apparatus 200. In an embodimentthe motion is a back and forth movement of the vehicle such that achange in the location of the vehicle is insignificant.

FIG. 3 illustrates a radar apparatus 300 according to an embodiment. Theradar apparatus 300 includes a transmit antenna unit 305 and a receiveantenna unit 320. A transmitter 310 is coupled to the transmit antennaunit 305. A control module 315 is coupled to the transmitter 310. Thereceive antenna unit 320 is coupled to a receiver 325. A mixer 330 iscoupled to the receiver 325 and to the transmitter 310. An analog todigital converter (ADC) 335 is coupled to the mixer 330 and an FFT (fastfourier transform) module 340 is coupled to the ADC 335. A signalprocessing unit 345 is coupled to the FFT module 340. The radarapparatus 300 may include one or more additional components known tothose skilled in the relevant art and are not discussed here forsimplicity of the description.

The operation of the radar apparatus 300 illustrated in FIG. 3 isexplained now. The transmit antenna unit 305 transmits an outbound RF(radio frequency) signal to a plurality of obstacles and the receiveantenna unit 320 receives an inbound RF signal from the obstacle. Theoutbound RF signal is scattered by the plurality of obstacles togenerate the inbound RF signal. The outbound RF signal includes aplurality of frames of the RF signal generated by the transmitter 310and the inbound RF signal includes a plurality of frames of the signalreceived from the plurality of obstacles. The control module 315provides a control signal to the transmitter 310. The transmitter 310generates the outbound RF signal and the receiver 325 receives theinbound RF signal from the receive antenna unit 320.

In one embodiment, the transmit antenna unit 305 includes one or moretransmit antennas coupled to the transmitter 310. The transmit antennaunit 305 is analogous to the transmit antenna unit 205 in the radarapparatus 200 in operation. The transmit antenna unit 305 thus includesa plurality of transmit antennas and each transmit antenna of theplurality of transmit antennas operate together to estimate position ofeach obstacle in a first range and each antenna in the plurality oftransmit antennas operate in a sequence to estimate position of eachobstacle in a second range, wherein first range is greater than thesecond range. In an embodiment, the receive antenna unit 320 includesone or more antennas coupled to the receiver 325.

In an embodiment, the receive antenna unit 320 is analogous to thereceive antenna unit 210 and thus includes a linear array of antenna andan additional antenna at a predefined offset from at least one antennain the linear array of antennas. In an embodiment, each antenna in thelinear array of antenna and the additional antenna has a separatereceiver path comprising receiver, mixer and ADC. Each receiver path iscoupled to the signal processing unit 345.

The mixer 330 receives the inbound RF signal from the receiver 325 andgenerates a demodulated signal. The ADC 335 receives the demodulatedsignal from the mixer 330 and generates a digital signal in response tothe demodulated signal. The FFT module 340 receives the digital signalfrom the ADC 335 and is configured to transform the digital signal froma time domain to a frequency domain. The signal processing unit 345 isconfigured to process the digital signal received from the FFT module340. The signal processing unit 345 is analogous to the signalprocessing unit 215 in operation. The signal processing unit 345 is usedin estimating position of a plurality of obstacles at a fixed distancefrom the radar apparatus 300 and having the same relative velocity withrespect to the radar apparatus 300. In one example, the receive antennaunit 100 is used to estimate the position of a plurality of obstacleswhich are at different distances and have different relative velocitieswith respect to the radar apparatus 300. For example, the receiveantenna unit 320 is used to estimate a position of two obstacle A and Bin which A is at 1 m and B is at 1.2 m from the radar apparatus and therelative velocity of A is 5 m/s and the relative velocity of B is 4.5m/s. In an additional example, the receive antenna unit 320 is used toestimate a position of two obstacles that are detected in different binsof a 2D FFT grid but their signals in the 2D FFT domain interfere witheach other. For example, a first obstacle which is detected in a firstbin of a 2D FFT grid can have an attenuated signal representing thefirst obstacle in a second bin. This attenuated signal interferes withposition estimation of a second obstacle detected in the second bin. Thesignal processing unit 345 estimates an azimuth angle and an elevationangle associated with each obstacle of the plurality of obstacle in thesame manner as performed by the signal processing unit 215. The signalprocessing unit 345 estimates an azimuth frequency, a complex amplitudeand a complex phasor associated with each obstacle by processing thedigital signal received from the FFT module 340 using the same method asused by the signal processing unit 215. Thus, the plurality of frames ofthe signal received from the plurality of obstacles at the linear arrayof antennas in the receive antenna unit 320 is used for estimating theazimuth frequency and the complex amplitude associated with eachobstacle and the plurality of frames of the signal received from theplurality of obstacles at the additional antenna in the receive antennaunit 320 is used for estimating the complex phasor associated with eachobstacle. This process is explained earlier with reference to FIG. 2(a)and therefore is not included herein for sake of brevity of description.In one example, all the components of the radar apparatus 300 areintegrated on a chip. In another example, all the components of theradar apparatus 300 except the signal processing unit 350 are integratedon a chip.

The radar apparatus 300 provides an efficient method to resolve theazimuth angle and elevation angle of two obstacles ‘m’ 255 and ‘n’ 260of the plurality of obstacles, when ‘m’ 255 and ‘n’ 260 are at a samedistance from the radar apparatus 300 and having the same relativevelocity with respect to the radar apparatus 300. Also, the radarapparatus 300 require less number of antennas than the conventionalmethods. With N antennas in the linear array of antennas and oneadditional antenna in the receive antenna unit 320, the radar apparatus300 is able to detect N−1 obstacles that are at the same range from theradar apparatus 300 and having the same relative velocity with respectto the radar apparatus 300.

The radar apparatus 300 also estimates the azimuth angle and elevationangle of these N−1 obstacles. Also, a processing requirement of thesignal processing unit 345 in the radar apparatus 300 is low as comparedto the conventional radar apparatus since the signal processing unit 345does not require any search, inversion of large matrices or findingeigenvalues and eigenvectors for estimating azimuth and elevationangles. The method of estimating the azimuth angle and the elevationangle in the signal processing unit 345 is less complex and also doesnot suffer from performance degradation due to false peaks/misseddetection of obstacles that severely effect search based solutionsespecially at low SNRs (signal to noise ratio).

The radar apparatus 300 provides an effective method to estimate theazimuth angle and the elevation angle even when an angular separation ofthe two obstacles ‘m’ 255 and ‘n’ 260 is small. The transmit antennaunit 305 includes a plurality of transmit antennas. Each transmitantenna of the plurality of transmit antennas operate together toestimate position of each obstacle in a first range and each antenna inthe plurality of transmit antennas operate in a sequence to estimateposition of each obstacle in a second range, wherein first range isgreater than the second range. This improves de-correlation of signalsreceived at the receive antenna unit 320 in the radar apparatus 300 andthus improves angle estimation performance.

In the foregoing discussion, the terms “connected” means at least eithera direct electrical connection between the devices connected or anindirect connection through one or more passive intermediary devices.The term “circuit” means at least either a single component or amultiplicity of passive or active components, that are connectedtogether to provide a desired function. The term “signal” means at leastone current, voltage, charge, data, or other signal. Also, the terms“connected to” or “connected with” (and the like) are intended todescribe either an indirect or direct electrical connection. Thus, if afirst device is coupled to a second device, that connection can bethrough a direct electrical connection, or through an indirectelectrical connection via other devices and connections. Also, the terms“inactivation” or “inactivated” or turn “OFF” or turned “OFF” is used todescribe a deactivation of a device, a component or a signal. The terms“activation” or “activated” or turned “ON” describes activation of adevice, a component or a signal.

It should be noted that reference throughout this specification tofeatures, advantages, or similar language does not imply that all of thefeatures and advantages should be or are in any single embodiment.Rather, language referring to the features and advantages is understoodto mean that a specific feature, advantage, or characteristic describedin connection with an embodiment is included in at least one embodimentof the present disclosure. Thus, discussion of the features andadvantages, and similar language, throughout this specification may, butdo not necessarily, refer to the same embodiment.

Further, the described features, advantages, and characteristics of thedisclosure may be combined in any suitable manner in one or moreembodiments. One skilled in the relevant art will recognize that thedisclosure can be practiced without one or more of the specific featuresor advantages of a particular embodiment. In other instances, additionalfeatures and advantages may be recognized in certain embodiments thatmay not be present in all embodiments of the disclosure.

One having ordinary skill in the art will understand that the presentdisclosure, as discussed above, may be practiced with steps and/oroperations in a different order, and/or with hardware elements inconfigurations which are different than those which are disclosed.Therefore, although the disclosure has been described based upon thesepreferred embodiments, it should be appreciated that certainmodifications, variations, and alternative constructions are apparentand well within the spirit and scope of the disclosure. In order todetermine the metes and bounds of the disclosure, therefore, referenceshould be made to the appended claims.

What is claimed is:
 1. A radar apparatus for estimating position of aplurality of obstacles, the radar apparatus comprising: a receiveantenna unit, the receive antenna unit comprising: a linear array ofantennas; and an additional antenna at a predefined offset from at leastone antenna in the linear array of antennas; and a signal processingunit, the signal processing unit configured to: estimate an azimuthfrequency associated with each obstacle of the plurality of obstaclesfrom a signal received from the plurality of obstacles at the lineararray of antennas; estimate a complex amplitude associated with eachobstacle from the estimated azimuth frequency associated with theplurality of obstacles and from the signal received from the pluralityof obstacles at the linear array of antennas; estimate a complex phasorassociated with each obstacle from the estimated complex amplitudeassociated with the plurality of obstacles and from a signal receivedfrom the plurality of obstacles at the additional antenna; and estimatean azimuth angle and an elevation angle associated with each obstaclefrom the estimated complex phasor associated with each obstacle and fromthe estimated azimuth frequency associated with each obstacle.
 2. Theradar apparatus of claim 1, wherein the plurality of obstacles have afixed distance and a fixed relative velocity with respect to the radarapparatus.
 3. The radar apparatus of claim 1, wherein a plurality offrames of the signal received from the plurality of obstacles at thelinear array of antennas is used for estimating the azimuth frequency;and wherein the complex amplitude is estimated for each frame of theplurality of frames.
 4. The radar apparatus of claim 1, wherein aplurality of frames of the signal received from the plurality ofobstacles at the additional antenna is used for estimating the complexphasor associated with each obstacle.
 5. The radar apparatus of claim 1,wherein the estimate of complex amplitude associated with each obstacleis one of a least squares estimate and a weighted least squaresestimate.
 6. The radar apparatus of claim 1, wherein the estimate of thecomplex phasor associated with each obstacle is one of a least squaresestimate and a weighted least squares estimate.
 7. The radar apparatusof claim 1, wherein the radar apparatus further comprises a transmitantenna unit, the transmit antenna unit further comprising a pluralityof transmit antennas and each transmit antenna of the plurality oftransmit antennas operate together to estimate position of each obstaclein a first range and each antenna in the plurality of transmit antennasoperate in a sequence to estimate position of each obstacle in a secondrange, wherein first range is greater than the second range.
 8. Theradar apparatus of claim 1 installed on a vehicle, wherein a motion inthe vehicle improves de-correlation in the radar apparatus.
 9. A methodof estimating position of a plurality of obstacles using a radarapparatus, the method comprising: estimating an azimuth frequencyassociated with each obstacle of the plurality of obstacles from asignal received from the plurality of obstacles at the radar apparatus;estimating a complex amplitude associated with each obstacle from theestimated azimuth frequency associated with the plurality of obstaclesand from the signal received from the plurality of obstacles at theradar apparatus; estimating a complex phasor associated with eachobstacle from the estimated complex amplitude associated with theplurality of obstacles and from the signal received from the pluralityof obstacles at the radar apparatus; and estimating an azimuth angle andan elevation angle associated with each obstacle from the estimatedcomplex phasor associated with each obstacle and from the estimatedazimuth frequency associated with each obstacle.
 10. The method of claim9, wherein the radar apparatus comprises a receive antenna unit, thereceive antenna unit further comprising: a linear array of antennas; andan additional antenna at a predefined offset from at least one antennain the linear array of antennas.
 11. The method of claim 9, whereinestimating the azimuth frequency further comprises estimating theazimuth frequency associated with each obstacle from a signal receivedfrom the plurality of obstacles at the linear array of antennas.
 12. Themethod of claim 9, wherein estimating the complex amplitude furthercomprises estimating the complex amplitude associated with each obstaclefrom the estimated azimuth frequency associated with the plurality ofobstacles and from the signal received from the plurality of obstaclesat the linear array of antennas.
 13. The method of claim 9, whereinestimating the complex phasor further comprises estimating the complexphasor associated with each obstacle from the estimated complexamplitude associated with the plurality of obstacles and from a signalreceived from the plurality of obstacles at the additional antenna. 14.The method of claim 9 further comprises estimating the azimuth frequencyand the complex amplitude associated with each obstacle from a pluralityof frames of the signal received from the plurality of obstacles at thelinear array of antennas.
 15. The method of claim 9 further comprisesestimating the complex phasor associated with each obstacle from aplurality of frames of the signal received from the plurality ofobstacles at the additional antenna.
 16. The method of claim 9, wherein:the estimate of complex amplitude associated with each obstacle is oneof a least squares estimate and a weighted least squares estimate; andthe estimate of the complex phasor associated with each obstacle is oneof a least squares estimate and a weighted least squares estimate. 17.The method of claim 9, wherein the radar apparatus comprises a transmitantenna unit, the transmit antenna unit further comprising a pluralityof transmit antennas and each transmit antenna of the plurality oftransmit antennas operate together to estimate position of each obstaclein a first range and each antenna in the plurality of transmit antennasoperate in a sequence to estimate position of each obstacle in a secondrange, wherein first range is greater than the second range.
 18. A radarapparatus for estimating position of a plurality of obstacles, the radarapparatus comprising: a transmit antenna unit; a transmitter coupled tothe transmit antenna unit and configured to generate the outbound RF(radio frequency) signal; a receive antenna unit; a receiver coupled tothe receive antenna unit and configured to receive the inbound RF signalfrom the receive antenna unit, wherein the outbound RF signal isscattered by the plurality of obstacles to generate the inbound RFsignal; a mixer coupled to the receiver and to the transmitter andconfigured to demodulate the inbound RF signal to generate a demodulatedsignal; an analog to digital converter (ADC) coupled to the mixer andconfigured to generate a digital signal in response to the demodulatedsignal received from the mixer; an FFT (fast fourier transform) modulecoupled to the ADC and configured to transform the digital signal from atime domain to a frequency domain; and a signal processing unit coupledto the FFT module and configured to process the digital signal, thesignal processing unit further configured to: estimate an azimuthfrequency associated with each obstacle of the plurality of obstaclesfrom the digital signal; estimate a complex amplitude associated witheach obstacle from the estimated azimuth frequency associated with theplurality of obstacles and from the digital signal; estimate a complexphasor associated with each obstacle from the estimated complexamplitude associated with the plurality of obstacles; and estimate anazimuth angle and an elevation angle associated with each obstacle fromthe estimated complex phasor associated with each obstacle and from theestimated azimuth frequency associated with each obstacle.
 19. The radarapparatus of claim 18, the receive antenna unit further comprising: alinear array of antennas; and an additional antenna at a predefinedoffset from at least one antenna in the linear array of antennas. 20.The radar apparatus of claim 18, wherein the complex phasor associatedwith each obstacle is estimated from a signal received from theplurality of obstacles at the additional antenna and from the estimatedcomplex amplitude associated with the plurality of obstacles.
 21. Theradar apparatus of claim 18, wherein the outbound RF signal comprises aplurality of frames of the RF signal generated by the transmitter andthe inbound RF signal comprises a plurality of frames of the signalreceived from the plurality of obstacles.
 22. The radar apparatus ofclaim 18, wherein: the plurality of frames of the signal received fromthe plurality of obstacles at the linear array of antennas is used forestimating the azimuth frequency and the complex amplitude associatedwith each obstacle; and the plurality of frames of the signal receivedfrom the plurality of obstacles at the additional antenna is used forestimating the complex phasor associated with each obstacle.
 23. Theradar apparatus of claim 18, wherein the transmit antenna unit furthercomprises a plurality of transmit antennas and each transmit antenna ofthe plurality of transmit antennas operate together to estimate positionof each obstacle in a first range and each antenna in the plurality oftransmit antennas operate in a sequence to estimate position of eachobstacle in a second range, wherein first range is greater than thesecond range.